2022 — On Bose-Einstein condensate in the Thomas-Fermi regime
Mathematical Physics, Analysis and Geometry
We study a system of trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form , for some and diverging as . We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if , condensation is preserved by the time evolution.
2021 — On some rigorous aspects of fragmented condensation
Nonlinearity
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to bosonic systems with infinitely many degrees of freedom, we address the problem of persistence of fragmented condensation. We show that the latter occurs in interacting systems, in the mean-field regime, and in the limit of large gap of the one-body Hamiltonian.
2016 — On the third Critical Speed for Rotating Bose-Einstein Condensates
Journal of Mathematical Physics
We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.
2021 — Kinetic Equations
Assistant Lecturer, Universität Basel
2020 — Analysis 1
Assistant Lecturer, Universität Basel
2020 — Introduction to Mathematical Quantum Theory
Assistant Lecturer, Universität Basel
2019 — Seminar Topics in Harmonic Analysis
Assistant Lecturer, Universität Basel
2011-2012 — Mathematical Analysis 4 - AM220
Tutoring activity, Roma Tre University (Italy)
2020 — Dynamics of Bose-Einstein Condensates in the Thomas-Fermi Regime
Seminar
Mathematical Institute LMU (Germany)